Statistics from Cornell's Northeast Regional Climate Center indicate that Ithaca, NY gets an average of 35.4" of rain each year, with a standard deviation of 4.2 Over a selected period of four years, let y represent the sample average amount of rainfall over that four-year period (n=4). Assume that rainfall amount in Ithaca, NY follows a Normal model. What is the probability that the sample average rainfall amount for the four-year period X is less than 30"? O a. 2571 Ob.1003 Oc. 9949 Od.0051
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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